Skip to main content
SpringerLink
Log in

Characterizations and representations of left and right hybrid (b, c)-inverses in rings

  • Original Paper
  • Published:
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

Let R be an associative ring with unity 1 and let \(a,b,c\in R\). In this paper, several characterizations for left and right hybrid (b, c)-inverses of a are derived. Moreover, their formulae are given by regularities of certain elements. Then, we give characterizations of right (b, c)-inverses and right annihilator (b, c)-inverses of the product of three elements. Finally, relations among the right hybrid (b, c)-inverse of paq, the right (qb, c)-inverse of aq and the right annihilator (b, cp)-inverse of aq are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ben-Israel, A., Greville, T.N.E.: Generalized Inverses: Theory and Applications, 2nd edn. Springer, New York (2003)

    MATH  Google Scholar 

  2. Drazin, M.P.: A class of outer generalized inverses. Linear Algebra Appl. 436, 1909–1923 (2012)

    Article  MathSciNet  Google Scholar 

  3. Drazin, M.P.: Left and right generalized inverses. Linear Algebra Appl. 510, 64–78 (2016)

    Article  MathSciNet  Google Scholar 

  4. Drazin, M.P.: Hybrid \((b,c)\)-inverses and three finiteness properties in rings and semigroups (2019) (for submission)

  5. Mary, X.: On generalized inverses and Green’s relations. Linear Algebra Appl. 434, 1836–1844 (2011)

    Article  MathSciNet  Google Scholar 

  6. Zhu, H.H.: Further results on several generalized inverses. Commun. Algebra 46, 3388–3396 (2018)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors are highly grateful to the referee for his/her valuable comments and suggestions which led to improvements of this paper. This research is supported by the National Natural Science Foundation of China (no. 11801124), China Postdoctoral Science Foundation (no. 2020M671068) and the Natural Science Foundation of Anhui Province (no. 1808085QA16) and Portuguese Funds through FCT (Fundca̧o para a Ciência e a Tecnologia) within the Projects UIDB/00013/2020 and UIDP/00013/2020.

Author information

Authors and Affiliations

  1. School of Mathematics, Hefei University of Technology, Hefei, 230009, China

    Huihui Zhu, Liyun Wu & Fei Peng

  2. CMAT-Centro de Matemática, Departamento de Matemática e Aplicações, Universidade do Minho, 4710-057, Braga, Portugal

    Pedro Patrício

Authors
  1. Huihui Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liyun Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fei Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pedro Patrício
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liyun Wu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhu, H., Wu, L., Peng, F. et al. Characterizations and representations of left and right hybrid (b, c)-inverses in rings. RACSAM 115, 22 (2021). https://doi.org/10.1007/s13398-020-00956-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13398-020-00956-7

Keywords

Mathematics Subject Classification

Search

Navigation